Abstract

This paper deals with an investigation of the effects of
diffraction and radiation on a submerged sphere in water of finite
depth d. We assume that the fluid is homogeneous, inviscid, and
incompressible, and the fluid motion is irrotational. In real
situations, the submerged sphere will experience six degrees of
freedom (i.e., motions); three translational and three rotational.
In this paper, however, we consider a very idealized
situation because of the complex nature of the physical problem.
Two important motions, namely, the surge (horizontal oscillations)
and the heave (vertical oscillations) motions are studied. Our
attention is mainly focused on the hydrodynamic coefficients of
these motions. The crux of the problem lies entirely on the
determination of these coefficients which are inherently related
to the determination of the motions of the submerged sphere in
regular waves. This type of problem is usually solved by using
potential theory, and mathematically, we look for the solution of
a velocity potential which satisfies Laplace's equation along with
the free surface, body surface, and bottom boundary conditions in
conjunction with a radiation condition. This boundary value
problem, in fact, consists of two separate problems: (a)
diffraction problem and (b) radiation problem.

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